3.18 A random sample of n 49 observations is drawn from a population with a mean

Question

3.18 A random sample of n 49 observations is drawn from a population with a mean equal to 24 and a standard EQuestion Help deviation equal to 14. a. Give the mean and standard deviation of the (repeated) sampling distribution x b. Describe the shape of the sampling distribution of x. Does your answer depend on the sample size? C. Calculate the standard normal z-score corresponding to a value of x 20.5. d. Calculate the standard normal z-score corresponding to a value of x - 26 Enter your answer in the edit flelds and then click Check Answer. Clear All 3 Pertainina 002 PM 10/24/2017 F12 PrtScr Insert Delete F10 F8 Backspace 7 8 9

Explanation / Answer

Answer to the question is as follows:

n = 49

Mean = 24

Stdev = 14

a. Mean of samling distribution = 24
Stdev of xbar = 14/sqrt(49) = 2

b. It is also normal, as the n>30, and the CLT theorm states that a sample from the population is normally distributed

c. z = (X-Mu)/(sigma/sqrt(n)) = (20.5-24)/(14/sqrt(49)) = -1.75

d. z = (X-Mu)/(sigma/sqrt(n)) = (26-24)/(14/sqrt(49)) = 1

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